QUESTION 3The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature x1, the number of days in the month x), the average productpurity x3, and the tons of product produced x4. The past year's historical data are available and are presented in the following table.24025249110031236290219095110452488274602587883016525919431672942625259997300808729684869626775248811027660259110528826150259010038238998If y= ao+@1X1+a2x2+@3X3+ a4X4 represents the regression model. What is the value of a4? Use 4 decimal places.

Given points are: y=a0+a1x1+a2x2+a3x3+aax4 represents the…

Answered: QUESTION 3 The electric power consumed…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The temperature of a certain chemical process is thought to be related to the time it takes for the process to reach completion. Out goal is to that relationship so that we can use it to predict TIME TO REACH COMPLETION at various TEMPERATURES. 14 trials are set up and the time for the process to complete is measured for each of the different temperatures. The data is presented here:(data is in the image added to the question as well as more questions to answer)
The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (in F) for that month. The past year's usage and temperatures are in the following table: Usage/ Month Temp. 1000 Month 21 185.79 July. 24 214.47 Aug. 32 288.03 Sept. 47 424.84 Oct. 50 454.58 Nov. 59 539.03 Dec. Jan. Feb. Mar. Apr. May June Temp. 68 74 62 50 41 30 Identify which are the independent and dependent variables. Usage/ 1000 621.55 675.06 562.03 452.93 369.95 273.98
What unit of analysis is reflected: "There is a relationship between unemployment rates and crime rates in a city such that cities with lower unemployment rates experience less crime."
The authors of a paper were interested in how the distance a deer mouse will travel for food is related to the distance from the food to the nearest pile of debris. Distances were measured in meters. The data and computer output are given below. Distance from Debris Distance Traveled 6.94 0.00 5.23 6.13 5.21 11.29 7.10 14.35 8.16 12.03 5.50 22.72 9.19 20.11 9.05 26.16 9.36 30.65 Simple Linear Regression Results: Dependent Variable: Traveled Independent Variable: Debris Sample size: 9 R (correlation coefficient) = 0.5657 R-sq = 0.32002088 Estimate of error standard deviation 8.670711 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept -7.6854587 13.332196 ≠ 0 7 -0.5764586 0.5824 Slope 3.2340908 1.7818117 ≠ 0 7 1.8150575 0.1124 a)What is the least squares regression line for the output given above? b) what is the predicted traveled distance given the distance from debris is 6.5 meters?
Q1. A study was conducted to investigate the relationship between premature birth and mental development at 12 months. The infant's birth weight was used as an index of prematurity. At age 12 months, the child's mental development was recorded. The results are shown below (the weights are in pounds): Birth 4 6 7 8 Weight(x) Developmental 85 Quotients(y) 88 87 94 96 Summary: n = 5, £x=30, £x² = 190, Ey= 450, Ey² = 40590, Exy = 2728 . a. Find the least square prediction equation, y on x. b. Obtain a 95% confidence interval for the average value of y when x 6.5 (i.e., a C.I. for E(y|x= 6.5)). c. Obtain the coefficient of correlation (r) and interpret the result. d. Test the hypothesis that H, :p= 0 vs. H, : p0. Use a =0.05.
Listed below are the numbers of deaths resulting from motor vehicle crashes. Let x represent the year, with 1975 coded as x = 1, 1980 coded as x = 6, 1985 coded as x = 11, and so on. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the best model to find the projected number of deaths for the year 2028. x (year) 1975 1980 1985 1990 1995 2000 2005 2010 D y (deaths) 44,533 51,122 43,809 44,590 41,798 41,960 43,436 32,697 (...) Choose the correct graph below. O A. O B. O C. D. 52000- 52000- 52000- 52000- DDDD 00 X X X X 32000+ 32000 32000+ 32000+ 0 40 0 40 0 40 0 40 What is the equation of the best model? Select the correct choice below and fill in the answer boxes to complete your choice. Enter only nonzero values. (Type integers or decimals rounded to three decimal places as needed.) O A. y= X B. y = + In x O C. y = + O D. X y=² O E. y = x² + X + Use the best model to find the projected number of such deaths for the year 2028. The projected…
Listed below are pulse rates (beats per minute) from samples of adult males and females. Does there appear to be a difference? Find the coefficient of variation for each of the two samples, then compare the variation. Male 89 70 60 69 68 51 66 55 81 70 60 64 98 54 65 D Female 66 83 80 71 72 86 87 88 90 89 92 72 86 78 79 The coefficient of variation for the male pulse rates is % (Type an integer or decimal rounded to one decimal place as needed.) The coefficient of variation for the female pulse rates is % (Type an integer or decimal rounded to one decimal place as needed.). Compare the variation. The coefficients of variation for each data set are EX Therefore, the male pulse rates vary the female pulse rates.
An outbreak of the deadly Ebola virus in 2002 and 2003 killed 91 of the 95 gorillas in 7 home ranges in the Congo. To study the spread of the virus, measure " distance" by the number of home ranges separating a group of gorillas from the first group infected. Here are data on distance and number of days until deaths began in each later group: Distance xx 2 5 4 4 4 6 Days yy 4 21 29 40 47 49 Use a calculator or software to find the following values. (a) Find the mean and standard deviation of xx. MEAN: STANDARD DEVIATION: (b) Find the mean and standard deviation of yy. MEAN: STANDARD DEVIATION: (c) Find the correlation rr between xx and yy. r:
The data used is from college campuses. The variables used in the analysis below include: crime, total campus crime; enroll, total enrollment; police, employed officers. Use the estimated OLS models to answer the questions below: Model A: In(crime) = -6.631 + 1.270ln(enroll), (1.034) (.110) .5804 n = 97; R² = Model B: In(crime) = -4.794+.923ln(enroll) +.516ln(police), (.144) (.149) (1.112) n = 97; R² = .632 Using Model A, test the null hypothesis that elasticity of crime with respect to enrollment is unit elastic, i.e. equal to one (against a two-sided alternative). What is the conclusion of your test using a significance level of .01? Reject Fail to reject O Not enough information.

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